*
Quite unfortunately, only Lecture 1 has good audio, while Lectures 2 and 3 came
out with extremely poor audio because of wrong settings so I removed their video,
and what is available is therefore only:

The
definition of entropy in one lecture

This short course is open to students and teachers who wish
to take a quick view (review) at how the general principles of thermodynamics
can be very effectively presented and taught in a rigorous way, by following the
treatment developed in the textbook

Gyftopoulos
& Beretta, Thermodynamics. Foundations and Applications
(originally published by Macmillan in 1991, now reprinted by Dover
in 2005, with problem
solutions). The treatment resolves conceptual loopholes and logical deficiencies
which are present in traditional treatments of thermodynamics, and it is
rigorous because it builds up a set of unambiguous definitions of all the basic
concepts needed in the exposition (system, property, state; nonequilibrium,
equilibrium, and stable equilibrium state; process, weight process, reversible
process; thermal reservoir).

The book has had a scientific role in the development of
thermodynamics, particularly because it has provided the first noncircular
definition of entropy, valid also for nonequilibrium states. It adopts the
statement of second law introduced by Hatsopoulos and Keenan in 1965, i.e., the
assertion of existence of a unique stable equilibrium state for each set of
values of the energy, the amounts of constituents, and the volume (and/or other
parameters), from which, of course, all the results of classical thermodynamics
unfold as rigorous results. But the simple and general extension to
nonequilibrium -- absent from traditional expositions and provided here avoiding
intentionally any statistical reasoning – makes the approach timely and
relevant for a variety of applications at the frontiers of the many fields of
science and engineering where nonequilibrium is the keyword. Moreover, by
introducing the ‘simple system’ model the book clearly separates the
concepts, results, and relations that hold for all well-defined systems,
including microscopic systems, from those which hold only for macroscopic and
mesoscopic systems, another restriction of traditional expositions.

The short course will illustrate how to present the essential
concepts in a small number of lectures suitable for an introduction at the
undergraduate level or an introductory review at the graduate level. Proofs and
details can be skipped because the students may find them in the book, if they
wish, but the important aspect remains that the approach is rigorous and
logically unambiguous. Because neither the students nor the teachers need to be
puzzled by the typical logical difficulties and ambiguities of the traditional
expositions (entropy defined in terms of heat and temperature, heat and
temperature defined in terms of entropy), they can all proceed quickly and
safely to the applications of interest.

Detailed outline

definitions of system, property, state, process, weight process

first law of thermodynamics and its consequences: definition of energy,
additivity, echangeability, and conservation of energy, energy balance equation